No, there is blood in your gums or blood spitting after brushing your teeth is not normal. However, if this is the case then you may have gum disease (periodontal disease) and it must be treated.
Gum disease is usually caused by the accumulation of dental plaque and tartar, mainly gingivitis and periodontitis. Gingivitis is a gingival inflammation that mainly reaches the surface. It can be shown by gum pain, bleeding and redness. You can usually treat gingivitis by improving your oral hygiene and regular cleaning and tartar tartar.
Periodontitis is a more advanced and more severe stage of gum disease. In addition to gingivitis symptoms, there may be gingival recession and tooth mobility (more or less teeth movement). This is a worrying situation that must be resolved immediately, usually by a dentist or a periodontal doctor (gum specialist). If this is not taken care of quickly, not only may all teeth be lost, but gum infection may enter the body and enter other organs such as the heart, leading to serious medical conditions.
It should be noted that there are other forms of gum disease that can be caused by hormonal changes, such as during pregnancy or systemic diseases such as diabetes.